F-86F CAP - indeed any CAP - would have given the Vulcan crews something to think about - particularly if the fighters were getting Bogey Dope and the Vulcan wasn’t.
F-86F vs Sea Harrier would have been interesting - but at some point AIM-9L may have made it less so. My understanding is the F-86 was guns only...other than some rocket only derivatives.
I remember from 607 that a SHAR was airborne at the time of at least one B.B. raid but not sure this constituted a sweep as such.